Detecting Lensing-Induced Diffraction in Astrophysical Gravitational Waves

Gravitational waves emitted from compact binary coalescence can be subject to wave diffraction if they are gravitationally lensed by an intervening mass clump whose Schwarzschild timescale matches the wave period. Waves in the ground-based frequency band $f\sim 10$--$10^3\,$Hz are sensitive to clumps with masses $M_E \sim 10^2$--$10^3\,M_\odot$ enclosed within the impact parameter. These can be the central parts of low mass $M_L \sim 10^3$--$10^6\,M_\odot$ dark matter halos, which are predicted in Cold Dark Matter scenarios but are challenging to observe. Neglecting finely-tuned impact parameters, we focus on lenses aligned generally on the Einstein scale for which multiple lensed images may not form in the case of an extended lens. In this case, diffraction induces amplitude and phase modulations whose sizes $\sim 10\%$--$20\%$ are small enough so that standard matched filtering with unlensed waveforms do not degrade, but are still detectable for events with high signal-to-noise ratio. We develop and test an agnostic detection method based on dynamic programming, which does not require a detailed model of the lensed waveforms. For pseudo-Jaffe lenses aligned up to the Einstein radius, we demonstrate that a pair of fully upgraded aLIGO/Virgo detectors can extract diffraction imprints from binary black hole mergers out to $z_s \sim 0.2$--$0.3$. The prospect will improve dramatically for a third-generation detector for which binary black hole mergers out to $z_s \sim 2$--$4$ will all become valuable sources.Comment: 14 pages including references; 8 figures; comments are welcom

Recovering stellar population parameters via two full-spectrum fitting algorithms in the absence of model uncertainties

Using mock spectra based on Vazdekis/MILES library fitted within the wavelength region 3600-7350\AA, we analyze the bias and scatter on the resulting physical parameters induced by the choice of fitting algorithms and observational uncertainties, but avoid effects of those model uncertainties. We consider two full-spectrum fitting codes: pPXF and STARLIGHT, in fitting for stellar population age, metallicity, mass-to-light ratio, and dust extinction. With pPXF we find that both the bias in the population parameters and the scatter in the recovered logarithmic values follows the expected trend. The bias increases for younger ages and systematically makes recovered ages older, $M_*/L_r$ larger and metallicities lower than the true values. For reference, at S/N=30, and for the worst case ($t=10^8$yr), the bias is 0.06 dex in $M_*/L_r$, 0.03 dex in both age and [M/H]. There is no significant dependence on either E(B-V) or the shape of the error spectrum. Moreover, the results are consistent for both our 1-SSP and 2-SSP tests. With the STARLIGHT algorithm, we find trends similar to pPXF, when the input E(B-V)<0.2 mag. However, with larger input E(B-V), the biases of the output parameter do not converge to zero even at the highest S/N and are strongly affected by the shape of the error spectra. This effect is particularly dramatic for youngest age, for which all population parameters can be strongly different from the input values, with significantly underestimated dust extinction and [M/H], and larger ages and $M_*/L_r$. Results degrade when moving from our 1-SSP to the 2-SSP tests. The STARLIGHT convergence to the true values can be improved by increasing Markov Chains and annealing loops to the "slow mode". For the same input spectrum, pPXF is about two order of magnitudes faster than STARLIGHT's "default mode" and about three order of magnitude faster than STARLIGHT's "slow mode".Comment: Accepted for publication in MNRAS. 17 pages, 17 figure

Analysis of surface polariton resonance for nanoparticles in elastic system

This paper is concerned with the analysis of surface polariton resonance for nanoparticles in linear elasticity. With the presence of nanoparticles, we first derive the perturbed displacement field associated to a given elastic source field. It is shown that the leading-order term of the perturbed elastic wave field is determined by the Neumann-Poinc\'are operator associated to the Lam\'e system. By analyzing the spectral properties of the aforesaid Neumann-Poinc\'are operator, we study the polariton resonance for the elastic system. The results may find applications in elastic wave imaging.Comment: 18 pages, comments are welcom